Solidify Modifier: how can I remove the inner mesh in a complex artifacts?
Not sure if I understand correctly but I think you may be misunderstanding what the Solidify modifier does.

It creates thickness on an object by duplication it's faces and offsetting the  by a specified distance along its normals. This makes it two sided, and creates a new set of faces virtually "duplicating" your object.

That being said you may use it for what you want by activating the options Fill Rim and Only Rim, that way only the distorted "cage" will be created, and no duplicates will be found.



Edit

See an example of an open area bellow where additional faces are created.

Have you tried the Smooth modifier instead? It wont create additional faces, and will have a similar offset effect, though it may cause some distortion in tighter corners.



Edit 2

Apparently the user's problem was with selecting linked geometry in edit mode.
You could apply the Solidify modifier with the Fill Rim option unchecked, and then enter edit mode and either hover one of the unwanted vertex and press L or select one of the unwanted vertex and press Ctrl + L to Select Linked